Use the Intermediate Value Theorem to prove that there is a solution The Marginal Value Theorem states that the best time t to leave a patch of cabbage is the solution t of the equation where is the travel time to the next cabbage patch and F(t) is the total amount of food gathered in one location in time t Suppose that 1 and F(t) 1 e t F(t) F'(1)

Question: Use the Intermediate Value Theorem to prove that there is a solution. The Marginal Value Theorem states that the best time t to leave a

Use the Intermediate Value Theorem to prove that there is a solution.

The Marginal Value Theorem states that the best time t to leave a patch of cabbage is the solution t of the equation

F(t) F'(1) =

where τ is the travel time to the next cabbage patch and F(t) is the total amount of food gathered in one location in time t. Suppose that τ = 1 and F(t) = 1 – e^-t.

F(t) F'(1) =

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